Comparing Linear Representations

Function 1 and function 2 can be represented by the description and the table shown below.

Function 1: Mike bought a computer for $1,100, and the computer’s value depreciates by $400 each year.

Function 2: Cathy deposits $650 in a new checking account.

Each week after that, the amount in her account changes according to the table below, in which y represents the total amount in the checking account as a function of the number of weeks, x.

Which statement is true of functions 1 and 2?

• Functions 1 and 2 both have positive slopes, but the y-intercept of function 1 is larger than that of function 2.

• Functions 1 and 2 both have negative slopes, but the y-intercept of function 1 is smaller than that of function 2.

• Function 1 has a positive slope and a smaller y-intercept, while function 2 has a negative slope and a larger y-intercept.

• Function 1 has a negative slope and a larger y-intercept, while function 2 has a positive slope and a smaller y-intercept

Which statement correctly compares the rates of change of functions 1 and 2?

• The slope of function 1 is-3 and the slope of function 2 is 2 so function 2 is changing at a faster rate.

• The slope of function 1 is 2 and the slope of function 2 is 3 so function 2 is changing at a faster rate.

• The slope of function 1 is -3 and the slope of function 2 is -2 so function 1 is changing at a faster rate.

• The slope of function 1 is -2 and the slope of function 2 is -3 so function 1 is changing at a faster rate.

Compared with the equation, which statement is true about the graph?

• The graph has a smaller slope and a lower y-intercept.

• The graph has a larger slope and a higher y-intercept.

• The graph has a larger slope and a lower y-intercept.

• The graph has a smaller slope and a higher y-intercept.

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Which statement is true about the y-intercepts of the functions?

• At least one of the functions does not have a y-intercept.

• Function 1 and Function 2 have y-intercepts that are equal.

• Function 1 has a y-intercept that is less than the y-intercept of Function 2.

• Function 1 has a y-intercept that is greater than the y-intercept of Function 2

Which representation shows a rate that is less than 60 miles per hour?

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• y = 70x, where x represents time in hours and y represents distance in miles

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• A line that passes through the origin and has a slope of 65

Pete’s Plumbing charges a flat fee of $28 for a house call and inspection and an additional $35 per hour for any onsite work. Which table represents a cost function with a greater hourly rate than these charges?

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Which mathematical sentence correctly compares the y-intercept of function A to the y-intercept of function B?

• 0=0

• 0<2

• 0<6

• 2=2

Which statement best compares the functions?

• The functions represent parallel lines.

• The functions represent the same line.

• The functions represent perpendicular lines.

• The functions represent intersecting lines that are not perpendicular.

Which statement best compares the functions?

• The vertex of function A is below the vertex of function B.

• The vertex of function A is above the vertex of function B.

• The vertex of function A is to the left of the vertex of function B.

• The vertex of function A is to the right of the vertex of function B.